Off the coast of Branford, Conn., the portfolio owned by Christine and Edmund Stoecklein includes many houses and a Jack Nicklaus-designed putting green

After spending years collecting a cluster of small islands off the Connecticut coast, a wealthy family has decided to put eight of the rocky islands on the market for $78 million.

Located in the Thimble Islands archipelago in Long Island Sound off the coast of Branford, nearly all of the islands for sale have homes on them, according to Shelly Tretter Lynch of Sotheby’s International Realty, one of the listing agents.

The largest, Rogers Island, is about 8 acres and includes a roughly 13,000-square-foot, 10-bedroom restored house built around 1900 as well as a swimming pool, a tennis court and a Jack Nicklaus-designed golf putting green and tees. Reachable by a 5- to 10- minute boat ride, the island also contains a four-bedroom guesthouse, an artist’s studio, two piers and a greenhouse.

The other islands for sale range from tiny undeveloped Reel Island to the roughly .8-acre Wheeler Island, which has an eight-bedroom house. A pedestrian bridge connects the East and West portions of Cut-in-Two Island, each of which has a house and guesthouse. The sale price also includes a 2.32-acre waterfront property on the mainland containing several houses and a private dock for boats traveling to and from the islands.

The properties are owned by Christine and Edmund Stoecklein. Ms. Stoecklein has spent years acquiring islands in the area: Her former husband John Svenningsen, founder of the party supplies company Amscan Holdings, purchased West Crib Island in the 1970s. After his death in 1997, she began buying up other islands, including Rogers Island in 2003 for $22.3 million, a record-setting price for the Thimbles. In total she spent more than $30 million to buy the islands, then spent millions more on renovations, infrastructure and landscaping, according to co-listing agent Bill Fandel of Telluride Sotheby’s International Realty.

The Stoeckleins use the islands to house friends and family in the summer, Mr. Fandel said, but they recently bought a home in Washington state, where they plan to spend more time. The family is selling all of the islands except West Crib, the first one they owned, he said.

In 2012 Ms. Stoecklein briefly listed two of the islands; they were removed from the market after failing to sell, and they’ve received further upgrades since then, Mr. Fandel said.

There are about 80 houses among the Thimble Islands, which became popular as a summer resort area in the late 19th century. It is difficult to price the islands because they rarely change hands, the listing agents said. Eleven-acre Potato Island, which isn’t owned by the Stoeckleins, is currently listed for $7.35 million.